Electrical Engineering XYZ MCQs
The number of parity bits in a 12-bit Hamming code is:
- 5
- 4
- 8
- 6
Correct answer:
In a Hamming code, if there are m parity bits, they can cover the data bits from 1 up to 2m. Subtracting out the parity bits, we are left with 2m−m−1 bits for data.
Given that in the problem there are 12 data bits, we want to find the smallest �m such that:
2m − m − 1
Now we can try different values of �m to find the minimum value that satisfies this inequality.
- For m=1: 21−1−1=0; which is less than 12.
- For m=2: 22−2−1=3; which is less than 12.
- For m=3: 23−3−1=4; which is less than 12.
- For m=4: 24−4−1=11; which is equal to 12.
So, m=4 satisfies the inequality. Therefore, a 12-bit Hamming code would have 4 parity bits.
Hence, the correct answer to the multiple-choice question is: 2. 4